Laws of Motion with Static Equilibrium

[Keithkent09]

Homework Statement

Find θ and W in the figure below where w1 = 16.0 N, w2 = 25.0 N, and α = 66.5°, assuming that the arrangement is at rest.

Homework Equations

T_1=25/sin(alpha)
F_x=-T_1cos(alpha)+T_2cos(theta)
F_y=T_1sin(alpha)+T_2sin(theta)-2

The Attempt at a Solution

I tried to use the above equations to solve for the three unknowns. First I found the tension of the string on the left, then plugged that into the second two equations to find the remaining values and I could not get the correct answers.

 

[kuruman]

T_1=25/sin(alpha)

Why is this true? What are tensions T₁ and T₂ in each rope?

 

[Keithkent09]

Sorry I meant that it is 16/sin(alpha).
This is because the vertical component of T_1 is 16 because of w_1. So using trig T_1=17.447. I am doing this the correct way and just making some kind of simple mistake?

 

[kuruman]

A pulley changes the direction of the tension without changing its magnitude. What is the tension in the piece of the leftmost rope that is hanging straight down?